Answer:
Short answer 0
Explanation:
We are intended to believe that the graph touches the x axis at exactly 1 place. If we write the vertex form of the equation, we get y = a*(x + 1)^2
The only problem left is what is "a"?
Use the y intercept to find that answer.
The y intercept from the graph is 0,2 which means that when x = 0, y = 2
x = 0
y = 2
2 = a(0 + 1)^2
2 = a(1)
a = 2
So the correct equation is y = 2(x+1)^2
Expand this to standard representation
y= 2(x^2 + 2x + 1) Remove the brackets
y=2x^2 + 4x + 2
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Answer: What is the discriminate?
a = 2
b = 4
c = 2
The discriminate formula is
sqrt(b^2 - 4*a*c)
sqrt(4^2 - 4(2*2)
sqrt(16 - 16)
sqrt(0)
0
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Rule and Answer: The discriminate is ALWAYS zero when the quadratic graph just touches the x axis. Opening up or opening down does not matter.